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18 Feb 2022, 21:37
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
45%
(medium)
Question Stats:
55% (01:03) correct
45%
(01:10)
wrong
based on 311
sessions
History
Date
Time
Result
Not Attempted Yet
How many trailing zeroes are there in 28! + 29! ?
A. 1
B. 3
C. 5
D. 6
E. 7
A. 1
B. 3
C. 5
D. 6
E. 7
18 Feb 2022, 23:26
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Great question that tests factoring skills
I came up with answer choice (D) but then realised why(E) is correct.
If you chose D, chances are you missed the factoring that is staring at you right in the face!
There are 2 steps to this problem
1. To get trailing zeroes - you basically need 10s or combinations of 2 x 5.
So working through 28! means going 1x2x3x4… etc. till 28.
There are technically six ‘5s’ from 1 to 25 - with an additional 5 coming from the number 25 itself (5x5).
You can pair each of these ‘5s’ with the any of 6 multiples of 2 from 1 to 28 to get combinations of 10s.
For example - 2, 4, 6,8,10,12 can all be broken as 2x and that 2 can be paired with 5s to get 10
So at first, it looks like the answer is (D) - 6
But don’t forget the next crucial step!
2. The question stem says 28! + 29!
29! = 28! x 29
So the question can be rewritten as 28!(1 +29) or “28! x 30”
Alas, we found an additional zero!
So the answer is (E) - 7 trailing zeroes at the end
Posted from my mobile device
I came up with answer choice (D) but then realised why(E) is correct.
If you chose D, chances are you missed the factoring that is staring at you right in the face!
There are 2 steps to this problem
1. To get trailing zeroes - you basically need 10s or combinations of 2 x 5.
So working through 28! means going 1x2x3x4… etc. till 28.
There are technically six ‘5s’ from 1 to 25 - with an additional 5 coming from the number 25 itself (5x5).
You can pair each of these ‘5s’ with the any of 6 multiples of 2 from 1 to 28 to get combinations of 10s.
For example - 2, 4, 6,8,10,12 can all be broken as 2x and that 2 can be paired with 5s to get 10
So at first, it looks like the answer is (D) - 6
But don’t forget the next crucial step!
2. The question stem says 28! + 29!
29! = 28! x 29
So the question can be rewritten as 28!(1 +29) or “28! x 30”
Alas, we found an additional zero!
So the answer is (E) - 7 trailing zeroes at the end
Posted from my mobile device
General Discussion
17 Aug 2023, 11:00
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number of trailing 0 will be the power of 5 in the expression
28!(1+29)
28! * 30
28/5 + 28/25 = 5 + 1 + 1 (30) = 7
28!(1+29)
28! * 30
28/5 + 28/25 = 5 + 1 + 1 (30) = 7
